How to Determine Velocity at Gear Center Using Point C?

  • #1
WhiteWolf98
89
8

Homework Statement



f9f2b36b52142b4cee9169ed9f521b20.png


Homework Equations


##v=\omega r##

The Attempt at a Solution


So, using the equation, one can work out the velocity at point ##B##.
##v_B=\omega_{AB} \cdot r_B##
##v_B=6(0.4)=2.4~ ms^{-1}##I then tried working out the angular velocity at point ##C## using the instantaneous centre of zero velocity (I'm not sure of this is the correct next step. I don't think it is). But this ends up giving:
##\cos60= \frac {0.6} {r_{B/IC}}##
##r_{B/IC}=1.2##

Using ##v=\omega r##, this gives the angular velocity at point ##C## as ##2~rad/s##. This can't be right though since the velocity comes out as ##0.2## using ##r=0.1~m##

The answer is ##1.04~ms^{-1}##
 

Attachments

  • f9f2b36b52142b4cee9169ed9f521b20.png
    f9f2b36b52142b4cee9169ed9f521b20.png
    24.2 KB · Views: 895
Physics news on Phys.org
  • #2
WhiteWolf98 said:
I then tried working out the angular velocity at point C using the instantaneous centre of zero velocity
Not sure what that means, or how you got the next equation.
Think about the velocity of C. What is the relationship between that and B's velocity?
 
  • #3
Could it be that ##v_C={v_B} \cos30##?
 
  • #4
WhiteWolf98 said:
Could it be that ##v_C={v_B} \cos30##?
Quite so.
 
  • #5
How can I use the velocity at point ##C## to work out the velocity at the centre of the gear?
 
  • #6
WhiteWolf98 said:
How can I use the velocity at point ##C## to work out the velocity at the centre of the gear?
When in doubt, make a quick sketch:
upload_2018-12-11_17-40-16.png
 

Attachments

  • upload_2018-12-11_17-40-16.png
    upload_2018-12-11_17-40-16.png
    1.3 KB · Views: 494
Back
Top